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Homework_5

# Homework_5 - b The set of strings of balanced parentheses...

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Theory of Computing Homework 5 CS 3810, Fall 2009 Due Friday, October 2 General guidelines: You may work with other people, as long as you write up your solution in your own words and understand everything you turn in. Make sure to justify your answers—they should be clear and concise, with no irrelevant information. Each problem should be submitted on a separate piece of paper. Please put your netid on your homework! 1. 4.2.6 by machine construction Show that the regular languages are closed under the following operations. a) min(L)={w|w is in L, but no proper prefix of w is in L}. b) max(L)={w|w is in L and for no x other than ε is wx in L}. c) init(L)={w|for some x, wx is in L}. Hint: It is easiest to start with a DFA for L and perform a construction to get the desired language. 2. 4.4.1 a) Draw the table of distinguishabilities for the automaton below. b) Construct the minimum-state equivalent DFA. 0 1 * A B A B A C C D B D D A E D F F G E G F G H G D 3. 4.1.1 b and d Prove that the following are not regular languages.

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Unformatted text preview: b) The set of strings of balanced parentheses. These are the strings of characters “(“ and “)” that can appear in a well-formed arithmetic expression. d) { } 0 1 2 | and are arbitrary integers n m n n m . CONTINUES ON NEXT PAGE Theory of Computing Homework 5 CS 3810, Fall 2009 Due Friday, October 2 4. 4.1.2 c, e, and h Prove that the following sets are not regular languages. c) { } 0 | is a power of 2 n n e) The set of strings of 0’s and 1’s that are of the form ww, that is, some string repeating. h) The set of strings of the form 1 n w , where w is a string of 0’s and 1’s of length n. 5. 4.2.13 Start with the fact that the language { } 0 1 0 1 | n n n n L n = ≥ is not a regular set. Prove the following languages not to be regular by transforming them, using opertions known to preserve regularity, to 0 1 n n L : a) { } 01 | i j i j ≠ b) { } 0 1 2 | n m n m n m-≥ ≥ ....
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